integration with partial fractions

[CalcGuy]

see attachment

did i do this right so far? the numbers are ugly usually meaning i did it wrong... i think i can reduce it some more too... but i didnt want to go thru the trouble if its already wrong... and im not really sure how id reduce it... im thinking that i might be able to use the property rln(a)=ln(a)^r

 

[BigGlenntheHeavy]

\(\displaystyle Your \ answer \ is \ correct, \ however \ if \ in \ doubt, \ take \ the \ derivative \ of \ your \ final \ answer\)

\(\displaystyle and \ if \ it \ is \ correct, \ then \ you'll \ get \ the \ original \ function \ back, \ for \ example:\)

\(\displaystyle D_x\bigg[\frac{41}{234}ln|2x-1|+\frac{32}{143}ln|x+6|+\frac{208}{99}ln|x-5|+C\bigg] \ = \ \frac{5x^{2}+21x-22}{(2x-1)(x^{2}+x-30)}\)

 

[Deleted member 4993]

see attachment

did i do this right so far? the numbers are ugly usually meaning i did it wrong... i think i can reduce it some more too... but i didnt want to go thru the trouble if its already wrong... and im not really sure how id reduce it... im thinking that i might be able to use the property rln(a)=ln(a)^r

You can check your work by differentiating your result.